Cosmological constant from the ghost: A toy model

Abstract

We suggest that the solution to the cosmological vacuum energy puzzle is linked to the infrared sector of the effective theory of gravity interacting with standard model fields. We propose a specific solvable two dimensional model where our proposal can be explicitly tested. We analyze the 2d Schwinger model on a 2-torus and in curved 2d space, mostly exploiting the properties of its topological susceptibility, its links with the nontrivial topology or deviations from spacetime flatness, and its relations to the real 4d world. The Kogut-Susskind ghost (which is a direct analogue of the Veneziano ghost in 4d) on a 2-torus and in curved 2d space plays a crucial role in the computation of the vacuum energy. The departure from Minkowski flatness, which is defined as the cosmological constant in our framework, is found to scale as $1/L$, where $L$ is the linear size of the torus. Therefore, in spite of the fact that the physical sector of 2d QED is represented by a single massive scalar particle, the deviation from Minkowski space is linear in $L$ rather than exponentially suppressed as one could na\"{\i}vely expect.